This invention relates to a magnetic system, and more particularly to a magnetic flux transmission system.
Conventionally, various types of electrical devices have been developed using magnets, transformers or choke coils etc., as devices for efficiently utilizing the magnetic flux generated thereby. For example, in transmitting magnetic flux to a fairly distant location, it is necessary to use a solenoid having a length about the same as the transmission distance. If the coil length is very great, this is uneconomic, and lacking in practicality.
The basic reasons for this will be explained below by a calculation concerning the reasons why magnetic flux cannot be transmitted over long distances. Referring to FIG. 1, when a current I flows in a circular circuit consisting of a coil of one turn at the leftmost end, the direction of the magnetic flux at the center point 0 is then the direction perpendicular to the plane of the circular circuit. In a vacuum, magnetic field dH of point 0 obtained from linear element ds of prescribed length can be found by the Biot-Savart Law by: EQU dH=[I/(4.pi.a.sup.2)]ds (1)
Consequently, the magnetic field H obtained from the complete circuit is: ##EQU1## where ds=2.pi.a. The above equation (2) gives the field obtained for one turn at the left most end in FIG. 1. However, clearly, in the case of n turns, EQU H=nI/2a (3)
The intensity of the magnetic field at a point P on the axis of the circular circuit is next determined. The magnetic field dH at point P obtained from linear element ds is perpendicular to ds and distance r, so, based on the object concept, the effective amount of the entire magnetic field is the component in the OP direction.
The component of dH in the OP direction = ##EQU2## If it is assumed that OP =x, EQU H(x)=Ia.sup.2 /[2(A.sup.2 +x.sup.2).sup.3/2 ] (5)
is obtained. If it is provisionally assumed that there are n circular circuit turns, then EQU H=nIa.sup.2 /[2(a.sup.2 +X.sup.2).sup.3/2 ] (6)
Consequently, the intensity of the magnetic field at a point other than on the axis cannot easily be found. However, the approximate magnitude of the magnetic field can be inferred from FIG. 2, as will be explained.
An example of a magnetic field created by a single-layer winding solenoid shall be used, for simplicity in calculation. If it is assumed that the number of turns per unit length of the solenoid is n, its radius is a, and that it is wound with uniform thickness on a cylinder, the intensity of the magnetic field at a point P on its center axis is: EQU dH=(nIa.sup.2 dx)/[2(a.sup.2 +x2).sup.3/2] ( 7)
where x=a cot.THETA., dH=-(1/2) nI sin .THETA.d.THETA., so: ##EQU3##
Consequently, if point P is in the neighborhood of the middle of a solenoid of sufficient length, cos.THETA..sub.1 =0, cos.THETA..sub.2 approximately equals + 1, so, from above equation (8), EQU H=nI (9)
and, at point 0 at the end of the solenoid, cos.THETA..sub.1 =0, cos.THETA..sub.2 approximately equals + 1, so, from equation (8): and, at end 0 of the solenoid, EQU H=(1/2) nI (10)
As shown in FIG. 2, there is a rapid reduction in the intensity of the magnetic field at the end of the solenoid. As is apparent from equation (9) and equation (10), it is one half that at the center. This fact means that, with a conventional magnetic flux generating device using an iron core, or in the case of an air-cored coil described above, at a distance beyond length L of the windings, the magnetic flux leaks to the outside. As shown in FIG. 3, this causes an abrupt decrease in the magnetic field, which makes transmission of magnetic flux over a long distance impossible.